Classical conditioning can be best understood by the example of Pavlov's dogs. Pavlov's dogs were discovered salivating by the mere sound of the people with food coming rather. In other words, they were reacting to a neutral stimulus. Operant conditioning, on the other hand, is more about reward and punishment (Donaldson 2008). Operant conditioning works because sometimes the subject is rewarded and sometimes not and this has found to be very successful (the most successful, in fact) in conditioning. For example, if one sometimes gives dogs food off their plate and sometimes not, the dog will be conditioned to wait always for the food because sometimes he gets it. The term 'mental illness' is a culturally bound term. What is considered a mental illness in western culture may not be considered a mental illness in eastern countries. For example, anorexia is a common mental illness in the United States, but it does not exist in certain parts of the world. Also, some mental illnesses may be more accepted in parts of the world rather than in others, so using the term 'mental illness' must be used carefully as it does not mean the same thing to everybody all across the world.

OCD (obsessive-compulsive disorder), depression,...

The DSM-IV-TR (2000) is a diagnostic manual that clinical practitioners use to diagnose mental disorders. In considering mental disorders and the DSM-IV, it is important to understand how mental disorders are seen and how they are constantly changing in terms of the way we see them. For example, fifty years ago the DSM had homosexuality in it as a mental disorder. Of course, we know today that homosexuality is not a mental illness, but we can see from this example the way that progress and thinking changes our perceptions of things. Likewise, there are many disorders that are now in the DSM that were not in their 50 years ago -- like gender identity disorder.
References

American Psychiatric Association. (2000). Diagnostic and statistical manual of mental disorders. (4th edition).

Donaldson, J. (2008). Oh, behave!: Dogs from Pavlov to Premack to Pinker. Dogwise Publishing.

Mitchell, S.A. & Black, M.J. (1996). Freud and beyond: A history of modern psychoanalytic thought. Basic Books.

Piaget, J. (2001). The psychology of intelligence. (2nd edition). Routledge.